摘要：Model selection and model averaging are popular approaches for handling modelinguncertainties. The existing literature offers a unified framework for variable selection via penalizedlikelihood and the tuning parameter selection is vital for consistent selection and optimal estimation.Few studies have explored the finite sample performances of the class of ordinary least squares (OLS)post-selection estimators with the tuning parameter determined by different selection approaches.We aim to supplement the literature by studying the class of OLS post-selection estimators. Inspiredby the shrinkage averaging estimator (SAE) and the Mallows model averaging (MMA) estimator,we further propose a shrinkage MMA (SMMA) estimator for averaging high-dimensional sparsemodels. Our Monte Carlo design features an expanding sparse parameter space and furtherconsiders the effect of the effective sample size and the degree of model sparsity on the finitesample performances of estimators. We find that the OLS post-smoothly clipped absolute deviation(SCAD) estimator with the tuning parameter selected by the Bayesian information criterion (BIC)in finite sample outperforms most penalized estimators and that the SMMA performs better whenaveraging high-dimensional sparse models.
关键词：Mallows criterion; model averaging; model selection; shrinkage; tuning parameter choice
